Scientists are interested in physical characteristics of bodies of water. Among these characteristics are waves and fluid flow, most commonly referred to as currents. Both of these physical characteristics serve as forcing mechanisms, which can largely influence activities in bodies of water. These activities include many biological processes, navigation, industrial applications, structural response evaluation, and weather to name a few.
The nature of currents and waves is often random in behavior and therefore a complete understanding requires an accurate means of measurement. One of the most common ways to quantify and describe this behavior is to perform location specific measurements.
Over the years, there have been several ways of measuring waves and currents. The variety of measurement approaches is partially due to the evolution of technology and partially due to the requirements to withstand different environmental conditions. The challenge of measuring currents and waves is that the environment itself is not particularly favorable for in situ measurements.
Doppler Current Measurements
Current measurements are increasingly performed using acoustic Doppler technology. Acoustic Doppler measurements of currents involve transmitting a pulse of acoustic energy of known frequency into a fluid of known sound speed and detecting the acoustic return, which reflects from acoustic-scattering particles in the fluid medium. The change in frequency of the detected pulse, or Doppler shift, is an indication of the fluid's speed in the direction of the propagating acoustic wave, or acoustic beam. Measuring the fluid velocity from three unique and known geometric directions presents a method of estimating the three-dimensional velocity. An estimate of the fluids velocity relative to the acoustic instrument can be determined by performing a standard coordinate transformation from the acoustic beam coordinates to any other standard coordinate system, such as xyz and east-north-up. In order to transform between coordinate systems, there is an assumption that the flow is uniform within the volume of fluid bounded by the acoustic beams.
Remotely measuring fluid motion from the instrument itself is a distinct advantage of acoustic Doppler velocity measurements. This fact allows for measuring flow characteristics at several distances from the instrument, and thus allows for a profile of the current velocity in a direction away from the Doppler instrument.
Wave Measurements
The measurement of surface waves applies to any large body of water. For simplicity, the following discussion will refer to this large body of water as an ocean, lake, or harbor; and the surface waves may be referred to as waves or ocean waves. Some special cases may include man made bodies of water such as laboratory water tanks.
Over the last several decades, there have been several instruments or approaches to measuring and characterizing waves. The characterization is most commonly done according to estimates of standard wave parameters such as height, period, and direction. Specific examples of these include significant height, maximum height, peak period, mean period, peak direction, mean direction, and directional spread. The estimates are a result of processing a time series of data. The time series are measurements of some kind of quantity that is directly relatable to surface waves. This quantity may be pressure, orbital velocities, surface slope, or surface displacement to name a few. Most of these measured quantities require some kind of transfer function that relates the measured quantity to the surface displacement.
Ocean waves are a random event in nature. Characterizing random events requires establishing an ensemble of measurements according to statistical theory. Measuring random yet periodic waves means that the length of the measurement record must be long enough to adequately represent the energy at the frequencies present. This duration usually ranges from several minutes to half an hour. It is assumed that ocean waves are statistically stationary during this measurement period.
The measurement ensembles are typically repeated at a regular cycle. This cycle is frequent enough to adequately track changes in the wave climate, and often ranges from half an hour to 3 hours. The total duration of a typical data collection exercise must be long enough to infer the wave climate for the location; the test would therefore contain several calm and storm events. A more thorough measurement exercise would be either long enough to include seasonal variations or permanently installed.
The most challenging aspect of the measurement requirements is that the instrument must be on site measuring waves on a regular schedule for extended periods of time. Exposure to a harsh ocean environment is therefore unavoidable and represents one of the clear challenges of measuring waves.
Storm events are quite harsh on ocean instrumentation. This is especially true for instrumentation exposed to wave forces. Given the requirements for wave measurements, the basic goals for the instrumentation is to have an accurate yet cost effective manner that is robust enough to handle its environment. Furthermore, the measurement device should not influence the wave characteristics. After considering these criteria, it is clear that all instruments have their strengths, weaknesses and optimum regime of operation.
Wave measurements can be divided into two broad descriptors. These are directional and non-directional. Directional estimates characterize not only where waves are coming from, but also the directional distribution of the wave energy; recall that waves are random and have contributions from many directions. Non-directional wave estimates characterize the energy distribution and commonly provide estimates of height and period.
Some of the more common approaches for determining non-directional wave estimates such as height and period include measurements of pressure, wave orbital velocity, surface elevation, surface velocity, or surface acceleration. Instrumentation with a sensor measuring these is often single point measurements, but may also be part of a system of sensors.
Determining wave direction characteristics is more complex and requires a system of measurements. A system may be composed of several measurements at one location; this type of system is usually three measurements that measure a vertical and two orthogonal/horizontal wave characteristics. This is called a “triple-point” measurement. Two of the more common triple-point systems are wave buoys and PUV instruments (pressure and two orthogonal, horizontal velocity measurements at one common point).
The other class of directional measurement system is array types of sensors. Sensor arrays may be any collection of measurements that have a horizontal separation that permits some form of array processing of the spatial lags associated with measurements of the waves passing through the array. Two of the more common arrays are pressure sensor arrays and current Doppler arrays.
Many of the measurements for waves require a special transfer function which allows the measurements to be transformed into a meaningful estimate of the variations of the ocean surface. The transfer function typically follows what is known as linear wave theory. Wave quantities that are measured below the surface (wave orbital velocity and pressure) require special attention since the signal attenuates dramatically from the surface towards the ocean floor. The degree to which the attenuation occurs depends on the wavelength of the waves we are measuring. As a rule, long waves have less attenuation than short waves. The exact manner in how this behaves is well described in linear wave theory but remains complex enough to trouble most newcomers to wave measurements.
An important detail to bear in mind about instruments that measure wave quantities at depth, is that the attenuation will ultimately influence the instrument's operational frequency band. The degree to which this occurs depends largely on the depth of the measurement.
Surface Instruments
a) Wave Staffs
Wave staffs are perhaps the most intuitive instruments to understand since they operate at the fluid-atmosphere interface and measure exactly what the user is interested, surface displacement. Often these wave gauges are a wire that runs vertically on a staff and outputs a voltage that is proportional to the length of submerged wire. Sampling the length of submerged wire for an interval of time provides a time history of the wave displacement. The measurement represents a change in surface elevation just at that point.
Wave staffs are an accurate instrument, but are not practical in most measurement scenarios. An example of the impracticality is in coastal waters where the depths are greater than a few meters. Here it is not realistic to have a rigid structure that can both handle the tough environment as well as small enough to not influence the waves themselves.
Some existing coastal structures may have staffs mounted to them. The structure influences the waves and this compromises the accuracy of the measurement. In light of these constraints, wave staffs are often found only in laboratories and wave tanks.
b) Wave Buoys
Wave buoys are similarly intuitive for the most part. These instruments measure motion directly on the surface. How they do this is a little more complicated and varied. Wave buoys are called “wave following” instruments, and as the name implies they “follow” the motion of a passing wave. There are several methods for measuring this motion; most measure acceleration (accelerometers) and rotation (tilt sensors). The more recent buoys include a GPS (Global Positioning System) receiver, which measures change of position.
Buoys offered the first practical and accurate in situ measurement of waves in the ocean, and for this reason buoys have become a standard. This is primarily attributed to the fact that for many years there was no other practical solution that could withstand the harsh ocean environment. However, wave buoys are not immune to the environmental conditions and the fact that buoys are deployed on the ocean's surface has taken its toll on buoys over the years; where storms, fishermen, and shipping traffic account for most of lost buoys. Still to date, buoys remain the only practical solution for measuring waves in depths greater than 100 meters.
The performance characteristics of buoys are quite good, and wave buoys have demonstrated the ability to accurately estimate standard wave parameters. Wave buoy measurement limitations are associated with long waves (period>20 seconds) and short waves (period<1.5 seconds). All buoys have a frequency for which they will resonate. This resonant frequency marks the upper frequency limit they are incapable of measuring waves. The resonant frequency is most influenced by the shape and size of the buoy. Therefore, most wave buoys are designed to have a resonant frequency, which lies in a frequency band outside the band of interest to most scientists. The more common wave buoys have a resonant frequency of 1 Hz. The effective upper frequency limit after filtering is approximately 0.7 Hz.
Sometimes motion sensors are placed on multi-function buoys to measure waves. The added physical demands (space and weight) of these other functions often lower the resonant frequency response of the buoy, and therefore complicate the buoy's ability to respond to wave motion. The result is a poorer description of wave characteristics. Some of these buoys include meteorological buoys that have towers on them or navigational buoys, which are designed to be stationary and not respond to waves.
Bottom Mounted Instruments
The other broad class of instruments is bottom mounted and these include a wide range of PUV type instruments and a handful of Doppler type instruments. The fact that they are bottom mounted provides one significant advantage and that is they are out of harms way.
c) PUV Type of Instruments
One of the most common types of bottom mounted instruments is the PUV type. The name “PUV” is simply the abbreviation of the quantities measured to estimate wave parameters. These are pressure (P) and the horizontal velocity components (U and V) associated with a wave's orbital motion. The method is a typical “triple-point” type of measurement. Triple-point measurements include a scalar quantity that can be used to infer surface displacement, and two orthogonal vector quantities to estimate wave direction. The three quantities are measured close together, relative to the length of the wave. The PUV class of instruments can naturally be any instrument that measures both pressure and the horizontal components of orbital velocity. For this reason, one can find a relatively wide range of vendors who offer this solution.
Non-directional estimates such as wave height and period are inferred from the energy distribution from either the pressure or velocity spectra. The directional estimates are calculated from the relationship between the velocity and pressure measurements.
Although the PUV method has many advantages, there exists a significant depth limitation for its performance. The depth limitation defines an upper frequency limitation for which the PUV can not estimate wave properties. The deeper the PUV instrument is positioned in the water, the lower this frequency limit becomes. The difficulty most engineers and scientist have with understanding this depth limitation is that there is not a unique depth at which the performance will cut off. The frequency limit is determined by the relationship between the wavelength and instrument's depth.
The limitation arises from the fact that both the quantities being measured (pressure and velocity) attenuate exponentially with depth and the rate at which the attenuation occurs depends on the wavelength.
Another way of looking at this problem is that the signal associated with long waves penetrates further down in the water column than the signal for shorter wavelength waves. This means longer waves (or lower frequency waves) can be measured in deeper waters than shorter waves (high frequency waves).
d) Pressure Sensor Arrays
Pressure sensor arrays are yet another method for measuring and estimating wave characteristics. Again, the pressure measurements are constrained by the same depth and wave frequency limitations as that of the PUV. The difference between the two is the method of estimating wave direction. Pressure sensors arrays are located below the surface and are separated horizontally at some distance from one another. The separation distance is generally half a wavelength of the shortest wave to resolve. This approach attempts to use the spatial lags between pressure measurements to resolve wave direction. This is an inverse problem and therefore necessitates special treatment. The solution most commonly used is a form of the Maximum Likelihood Method (MLM). The MLM solution determines the most probable direction that minimizes the error from the cross spectra of the measurements. The MLM solution is not limited to pressure sensors but can be any array of spatially separated wave measurements. These measurements include, but are not limited to surface slope, surface position, accelerations, and orbital velocities
In addition to the limitation imposed by the attenuation of the wave properties, there is another frequency limitation that is associated with the spatial size of the array itself. Wave directions can only be resolved for waves that have a wavelength that is longer than twice the horizontal distance of the closest array measurements.
e) Doppler Current Profilers
Current profilers that employ the acoustic Doppler effect are yet another type of bottom mounted wave measurement instrument. These instruments were initially used to profile currents but can also measure the local orbital currents created by waves. One clear advantage is that the depth limitation of the PUV subsurface instruments is partially circumvented by measuring the orbital wave velocities near the ocean surface, where wave motion is less attenuated. This means the instrument can measure more of the short wave spectrum than a PUV instrument deployed at the same depth. A complication is that this approach no longer measures the orbital velocities at one location but in three or more spatially separated locations.
The measurement locations or cells construct an array projected up near the surface. Therefore, the typical procedure for estimating wave direction (and other wave properties) is similar to the solution for the pressure sensor array; both may use the Maximum Likelihood Method. The array of Doppler measurements is mathematically more complicated since each of these cells has a unique orientation relative to the incident waves and therefore a unique response. The response of the measurements is necessary for the complete solution.
The complexity of the solution lies in the fact that the direction of the waves is not known beforehand and the response of the measurements are directionally dependent. This means the solution requires solving the direction first. The stated problem again is an inverse problem, which is why the MLM is used. The results prove to be quite good under most situations. The solution is particularly good for resolving waves from two unique directions having the same frequency.
It is important to note that this is a two step procedure for processing data from Doppler type of instruments that use the MLM. First the directional distribution of wave energy must be calculated, after which the non-directional energy distribution can be determined. This is because the non-directional spectra and parameters are inferred from the orbital velocity measurements and the transformation to surface displacement requires the directional dependent transfer function to be determined first.
The MLM solution requires that the measurements do not have high coherence. High coherence in wave measurements occurs when the spatial lags between measurements are small or when the horizontal spatial separation is small relative to the wavelength. This can be further complicated if the measurement array is overpopulated with several measurement locations, some of which having high coherence with one another. The inversion process becomes increasingly unstable when the described situation occurs. An example of such an array would be an array that has numerous array elements where the separation is small relative to the wavelength of the wave being measured.
Another example where the MLM solution is not appropriate would be if the instrument is on a moving platform. In such a situation the position of the measurement cells would be constantly moving over the course of the measurement period. The number of degrees of freedom resulting from measurements at several different locations (due to platform motion) would increase to a point where the MLM approach would be either unstable or computationally prohibitive. In summary, the MLM solution is an accurate solution; however, it is complex and the various limits of its use must be well understood prior to implementation.
f) Acoustic Surface Tracking (AST)
Doppler instruments which measure near surface orbital velocities from the bottom do extend the upper frequency range for bottom mounted wave instruments. Unfortunately, there remains a depth dependent upper frequency limit for these instruments as well. The limit is imposed by the spatial relationship between the wavelength and the spacing between measurements. As a rule, the upper frequency limit for Doppler profiler arrays exists when the frequency associated with waves having a wavelength that is shorter than two times the spacing of the two nearest array elements. This upper frequency limit becomes more restrictive as the instrument is positioned at greater depths and the measurement positions become more separated in space. Deployments in greater depths lead to larger separation distances. As a result this limits Doppler profilers to the measurement of only long waves (low frequency) or deployments in coastal depths. The constraints imposed by the relationship between array size and wavelength not only effects the upper frequency limit of the directional wave solution but also the upper frequency limit of the non-directional solution. This means the solution neglects the shortest waves from the total estimate. The resulting effect of this is usually an underestimation of the true wave height.
One way to get around the limits for non-directional wave estimates is to directly measure the position of the ocean surface. This can be done using acoustic ranging from the instrument to the surface. This is also known as echo ranging which is common to boat mounted depth sounders. The difference here is that this technique measures the continuous change of the surface position, and therefore it is referred to as acoustic surface tracking (AST). The distance can be directly estimated from knowing the speed of sound in the fluid medium and the time of travel between transmission and reception of the acoustic pulse. Acoustic surface tracking measures surface displacement at one position, and therefore it is limited to non-directional waves estimates when used as an independent estimator.
The acoustic surface tracking has two very distinct advantages over the other bottom mounted wave measurement methods. The first is that acoustic surface tracking is a direct measure of the waves and does not require a transfer function to infer surface displacement. The second advantage is that it does not have a depth dependent frequency limit as the pressure and velocity measurements have. The result is more accurate wave measurements and that the sensor itself can be deployed at greater depths.
The Search for a Depth Independent Wave Measurement Solution
The challenges of measuring waves are highlighted with each of the techniques discussed. First is the problem of exposure of instrumentation on or near the ocean surface. This can be overcome by moving the instrument to a subsurface position that allows it to remotely sense or measure the surface waves. The logical option is to move the instrument below the ocean surface. This location has diminished wave forcing and no exposure to shipping traffic.
Subsurface mounted sensors such as the combined pressure-velocity (PUV) alleviate the issue of instrument loss due to high exposure on the ocean surface. The method is still limited to low frequency waves and therefore it remains a viable option for relatively shallow deployment depths in the water column.
The Doppler profiler class of combined current profiler and wave measurement instruments improves upon the limits of the PUV method since it is capable of measuring wave induced currents up near the surface where the signal is strong. This allows the bottom-mounted instrument to operate at a greater depth than the PUV type of instruments. The problem with measuring wave orbital velocity is that the approach requires a computational intensive solution known as the Maximum Likelihood Method (MLM) to estimate the directional distribution. Additionally, the Doppler profiler still has two limits. The first is that it has an upper frequency limit. The second limit is that the wave directional processing method, the MLM, requires measurements on a stationary platform so that the velocity measurements are made at a repeatable location during the ensemble measurement cycle. Therefore, the current profiler using MLM processing can not be placed on a moving platform such as a subsurface buoy.
Therefore, a need exists for a subsurface mounted instrument that circumvents the attenuation of wave properties as the current profiler does, yet is simplistic like the PUV solution so that it may be mounted on a moving platform (e.g. subsurface buoy).
The inventors have recognized the following. A need exists to measure and estimate surface wave directional characteristics and non-directional characteristics. The estimates must be accurate for the frequency range of waves commonly known as gravity waves. The instrument must be below the surface and out of harms way. Ideally, the instrument must be able to measure wave properties from a moving platform such that there is a tractable directional solution from the raw wave data. The platform could be a subsurface buoy. The advantage of subsurface measurements is that it is not depth limited but can be used for full ocean depths. The system would permit an instrument to measure waves in all waters of the world with an appropriate mooring system and subsurface buoy, and therefore not limit stationary Doppler instruments to shallow coastal waters.